Defect type classifying method

ABSTRACT

The invention relates to a method for non-destructive testing of materials, in which at least two differently guided waves (modes) are produced in the solid body, each at at least one specified angle, the measured reflection values are placed in relation to a reference echo in order to obtain a relative reflection value, and the relative reflection values of the individual modes are again placed in relation to one another, thereby enabling the size and type of the defects to be determined.

This application is a continuation of application Ser. No. 09/273,442,filed Mar. 22, 1999 now abandoned, which application(s) are incorporatedherein by reference.

FIELD OF THE INVENTION

The invention relates to a method for non-destructive testing ofmaterials.

BACKGROUND AND PRIOR ART

Such methods are used for testing rods, wires or plates.

One known method for non-destructive testing of materials is the eddycurrent method. In this method defects in materials are detected by theproduction of a magnetic field by induction. This method is also used inwire testing equipment.

It is known, for example, to use rotary testing equipment for testingwire. In testing wire with rotary testing equipment a free ultrasonicwave is produced in the material, the reflection echo of which at thedefect in the material can be detected.

However, external defects, which make up the greater part of the defectsin materials, cannot be detected by this method. Moreover, free wavescannot be produced in all materials. Hence, for example, materialtesting using a free wave is not possible in wires having a diameterless than 15 mm.

A known ultrasonic testing method makes use of a one-dimensional wave(mode) which is generated by means of a piezoelectric transducer. By aone- or two-dimensionally guided ultrasonic wave is meant an elasticwave of which the wavelengths in one or two dimensions respectively arecomparable to or large compared with the linear dimensions of the bodybeing measured. Parts of the boundary surface are constantly ininteraction with the wave and thus cause guidance of the wave along thisboundary surface. The body thereby acts as a wave guide.

The reflection echo of the wave can be detected and then providesinformation about the existence of a defect in the material. From theamplitude of the echo some evidence of the size of the defect can alsobe derived. This evidence is however based on experiment and estimatedvalues and frequently does not agree with the actual facts. Falseestimates are often attributable to spurious echoes, for example theecho from the outer wall of the material or echoes from other soundreflectors.

From German published patent application 41 33 648 it is known to testrods with two-dimensionally guided bar waves. This enables sensitiveinvestigation of defects and determination of their size to beperformed.

By evaluation of the amplitude, the course and the damping of the wavereflection at the defect a cross-sectional area of the defect can becalculated by means of the equivalent defect method. While the measuredreflection value includes implicit information about the size and typeof the defect, it is not possible to gain information about the type ofdefect, i.e. the eccentricity of the defect, since there is no known wayof forming a relationship between the measured values and theeccentricity of the defect. All attempts to classify types of defecthave therefore failed.

In testing strip using one-dimensionally guided plate waves (“Lambmodes”) the applicant has already attempted, by the use of a system witha guided wave which is beamed into the test piece using two angles ofincidence, to derive the eccentricity of the defect in the material fromthe two echoes which are detected. However, these attempts have notyielded any success because of the concrete properties of the material.

OBJECT OF THE INVENTION

The object of the invention is to provide a method for non-destructivetesting of materials which makes determination of the size of the defectand classification of the type of the defect possible.

A further object is to enable the type of defect to be quicklydetermined.

SUMMARY OF THE INVENTION

To this end, in accordance with the invention in a method for testingsolid bodies using guided ultrasonic waves a first and a second guidedultrasonic wave are produced in a solid body by means of an ultrasonictransmitter, reflection waves of the first and second ultrasonic wavesare detected by an ultrasonic receiver and structures or defects in thematerial of the solid body are determined by combination of the detectedvalues of the first wave and the detected values of the second wave.

In an embodiment of the invention at least two differently guided waves(modes) are produced in the solid body, each at at least one specifiedangle, the measured reflection values are placed in relation to areference echo in order to obtain a relative reflection value, and therelative reflection values of the individual modes are placed inrelation to one another, thereby enabling the size and type of thedefects to be determined.

Each measured value of each mode thus contains coupled information aboutthe size of the defect and its type. By combination of the informationin two guided waves the respective values for the size and type of thedefect can be determined separately and independently of one another byelimination of the respective other value.

The guided wave is first of all beamed in so that a reflection value isobtained which contains the defect echo and a reference echo. This canfor example be the back wall echo of a measured plate. The back wallecho can be distinguished from the defect echo since it has a longertransit time. By means of the back wall echo and the defect echo therelative defect echo of each mode can be determined.

As reference echo any sound reflector can be used, for example a pointat which a wire deflection pulley presses on the wire. Preferably thelargest detectable signal is used as reference echo.

The relative defect echo is measured for two different guided waves(modes). The measured values are entered into the implied functions ofthe type and area of the defect which hold for the type and mode of thewave.

From the combination of suitable functions of the selected modes, whichcan be determined by decoupling and scalarisation of the wave equationsfor the components of the particle displacement vector, the value forthe type and size of the defect can be determined by computation foreach kind of guided wave (Rayleigh waves, plate waves, bar waves, tubewaves).

Since a time-consuming calculation is involved, and in the testing ofmaterials, for example in the ultrasonic testing of cold-rolled steelstrip, continuous investigation of defects in real time on the runningstrip is desired, in order to speed up the investigation of defects thereflection values can be calculated for a desired number of sizes andtypes of defect before the measuring procedure, so that during themeasurement only a comparison of the measured reflection values with thecalculated reflection values is necessary, so that the detected defectscan quickly be evaluated as to type and size.

To increase the precision of the measuring and testing system theboundary conditions at the surface of the defect, i.e. the normalcomponents of the stress tensor at the free surfaces of the material,can be taken into account. For if the boundary value problem is nottaken into consideration there is some deviation of the measuredreflection value and of the defect value determined therefrom from theactual size and type of the defect, since it is first of all assumedthat there is complete reflection from the defect and the actual size ofthe defect—or the deviation of the defect reflection from the completereflection due to the boundary value—is only estimated from experimentalvalues.

To take account of the boundary conditions actually obtaining, whichlead to a falsification of the reflection of the defect, the boundaryconditions must enter directly into the defect calculation. For thispurpose the tensor boundary conditions are first of all scalarised bysuitable breakdown of the vector for the particle displacement intothree linear independent partial vectors and by use of three suitablescalar potentials.

Since a complete decoupling for the boundary conditions is not possible,an approximation method known from quantum mechanics is used in order toobtain values satisfactory for practical purposes. It is surprisinglyfound that by means of the perturbation calculation a good defectclassification is already obtained with a first order approximation.

BRIEF DESCRIPTION OF THE DRAWING

The invention will be described in more detail below, by way of example,with reference to an embodiment shown in the FIGURE, which shows twotransmitter/receiver pairs disposed above a steel strip.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

An example of the use of the method in accordance with the invention fordetecting defects in cold-rolled steel strip using two plate wave modesis described below, wherein the starting point is the propagation of anelastic plate wave in an elastic, undamped, homogeneous,non-piezoelectric solid body. Tube or bar waves can also be used.

With regard to construction, putting the invention into practice firstrequires an arrangement of the ultrasonic transmitter and receiver whichpermits propagation of the guided wave in the plate and in whichtransmitter and receiver cones overlap in the respective intensitymaximum.

Such an arrangement is shown in the drawing, in which pairs 1, 2; 3, 4of transmitters E and receivers R are disposed above a steel strip 5 ofa cold rolling mill train at a specific angle such that the sound cones6, 8 intersect the receiver cones 7, 9 in the intensity maximum.Receivers and transmitters are disposed at a transducer spacing fromcentre to centre of the transducers of 60 mm, a transducer width of 50mm each and a wavelength of 4 mm at a distance of 0.4 mm from the steelstrip, each at 3.5° to the vertical. The angle is selected so that thesound beam is almost free from divergence.

The value measured at each receiver is first brought into relation withthe measured reference echo. On the basis of the followingconsiderations, and after correction for damping and divergence due todistance, this relative value, in combination with the relative measuredvalue of the other receiver, allows the type and size of defects to bedetermined: for steel strip it is preferred to use SH modes and Lambmodes.

Let a plate wave propagate in a homogeneous, isotropic, undamped,nonpiezoelectric, elastic plate of constant thickness d. Let theCartesian coordinate system (x₁, x₂, x₃ with the normal unit vectors e₁,e₂, e₃ to describe this wave propagation be selected such that the soundpropagation takes place in the x₁ direction, let the two plate surfaceslie parallel and symmetrical to the plane x₂=0 and let the plate itselfbe characterised by the dimensional relationship −d/2≦x₂≦+d/2.

If, to formulate the boundary value problem and in all furthercalculations, we make use of tensor calculus, and time is denoted by t,thickness by ρ, the stress tensor by T, the particle displacement vectorby u and the force density vector by f, then by use of the Λ operator weobtain for the plate wave the fundamental dynamic equation:$\begin{matrix}{{\nabla{\cdot T}} = {{\rho\quad\frac{\partial^{2}\quad}{\partial t^{2}}\quad u} - f}} & (1)\end{matrix}$and the material equation:T=μ[(∇u)+(∇u)^(T)]+λ(∇·u)1  (2)

Let the source of the plate wave be located at x₁=−∞. Then finally:f≡0  (3)

From (1), (2) and (3) the following equation of motion then follows atonce for the particle displacement vector: $\begin{matrix}{{{\mu\quad\Delta\quad u} + {\left( {\mu + \lambda} \right){\nabla\left( {\nabla{\cdot u}} \right)}} - {\rho\quad\frac{{\partial\,^{2}}\quad}{\partial t^{2}}\quad u}} = 0} & (4)\end{matrix}$

By introducing three suitable potentials ν, P, Π this equation of motioncan be split up into three decoupled wave equations.

The boundary conditions for the propagation problem of the monochromaticelastic plate waves are given by the requirement of identicaldisappearance of the normal components of the stress tensor T at the two“free” surfaces.

One thus obtains directly: $\begin{matrix}{\left( {T \cdot e_{2}} \right)_{x_{2} = {- \frac{d}{2}}} \equiv {0\bigwedge\left( {T \cdot e_{2}} \right)_{x_{2} = {+ \frac{d}{2}}}} \equiv 0} & (5)\end{matrix}$

From (5) there follows, in view of (2), the formulation of the boundaryconditions for the particle displacement vector u as: $\begin{matrix}\begin{matrix}{\left( {{\partial_{2}u_{1}} + {\partial_{1}u_{2}}} \right)_{x_{2} = {- \frac{d}{2}}} \equiv 0} & \bigwedge & {\left( {{\partial_{2}u_{1}} + {\partial_{1}u_{2}}} \right)_{x_{2} = {+ \frac{d}{2}}} \equiv 0} & \bigwedge \\{\left( {{\lambda\quad{\partial_{1}u_{1}}} + {\left( {{2\quad\mu} + \lambda} \right)\quad{\partial_{2}u_{2}}}} \right)_{x_{2} = {- \frac{d}{2}}} \equiv 0} & \bigwedge & {\left( {{\lambda\quad{\partial_{1}u_{1}}} + {\left( {{2\quad\mu} + \lambda} \right)\quad{\partial_{2}u_{2}}}} \right)_{x_{2} = {+ \frac{d}{2}}} \equiv 0} & \bigwedge \\{\left( {\partial_{2}u_{3}} \right)_{x_{2} = {- \frac{d}{2}}} \equiv 0} & \bigwedge & {\left( {\partial_{2}u_{3}} \right)_{x_{2} = {+ \frac{d}{2}}} \equiv 0} & ;\end{matrix} & (6)\end{matrix}$

The boundary conditions (6) can be scalarised in just the same way asthe equation of motion (4), by introducing the three scalar potentialsν, P, Π, but the decoupling is only partial: the potentials ν and Premain coupled together, while the potential Π and the associatedpartial solution of the boundary value problem is completely decoupled.

As a solution of the boundary value problem in plates the plate wavesare obtained: the eigensolutions of the coupled boundary value problemare called Lamb modes, the eigensolutions which are associated with thepotential Π are called SH modes.

SH Modes.

The SH modes (SH=shear horizontal−shear waves polarised horizontal tothe plate surface) are characterised in that the particle displacementvector is always parallel to the plate surface. The SH modes are not tobe confused with the freely propagating shear waves, which are sometimescalled SH waves. Only for the lowest SH mode (n=0) do the particleexcursions agree, that is to say, only then does the SH wave correspondto the mode SS₀.

As eigenvalue equation (“dispersion equation”) for the SH modes there isobtained, for the dimensionless lateral coordinates of the wave numbervector of the transverse wave which produces the plate wave:$\begin{matrix}{\gamma_{T} = {{\frac{n\quad\pi}{2}\bigwedge n} \in {\overset{\sim}{O}}_{0}}} & (7)\end{matrix}$

Since as plate waves the SH modes belong to the class ofone-dimensionally guided waves, the lateral coordinate of the wavenumber vector k_(T) can—as can be seen from (7)—only assume discretevalues. Here the eigenfunctions for the eigenvalues with aneven-numbered index n represent the class of the symmetrical SH modesand the eigenfunctions for the eigenvalues with an odd-numbered index nrepresent the class of the antisymmetrical SH modes.

The particle displacement vector for the special case of the symmetricalSH mode SS₀ is given by:u ^((ss) ⁰ ⁾ =A ^((ss) ⁰ ⁾cos [k(x ₁ −c _(T) t)]e ₃  (8)

From this the real, time-dependent acoustic Poynting vector for thespecial case of the symmetrical SH modes SS₀ is obtained as:P ^((ss) ⁰ ⁾ =ρc _(T) ³ k ² A ^((ss) ⁰ ⁾²sin² [k(x ₁ −c _(T) t)]e ₁  (9)

The calculation of the reflection coefficient of a mode for a defectposition is now carried out by the methods of the perturbation theory:as a zeroth approximation it is first assumed that the respective modeis only perturbed by the defect insofar as the acoustic power flowdensity arriving at the defect position is reflected by the crosssection of the defect completely, without divergence and without modeconversion. The first approximation is obtained by assuming that theguided waves can be represented as a superposition of the unperturbedincident wave and an interference wave, which is partly reflected andpartly transmitted. The interference wave is calculated by meeting theadditional boundary condition at the defect surface. Here modeconversion and divergence of the beam of sound waves inevitably occur.

If we take as the model defect a rectangle with the relative length ofside, the relative height 0 and the relative eccentricity γ, then as azeroth approximation the reflection factor for the special case of thesymmetrical SH mode SS₀ is: $\begin{matrix}{R^{({SS}_{0})} = \sqrt{\eta\quad\zeta}} & (10)\end{matrix}$

Since the formula (10) for the virtual reflection factor of thesymmetrical SH mode SS₀ of the plane model defect rectangle onlycontains the parameters relative defect length . and relative defectheight 0, but not the parameter relative defect eccentricity γ, althoughdefect detection is possible with the symmetrical SH mode SS₀ alone,classification of the type of the defect is not possible.

For the symmetrical SH modes SS_(m) with m>0 the corresponding formulais: $\begin{matrix}{R^{({SS}_{m})} = \sqrt{\eta\quad{\zeta\left\lbrack {1 + \frac{\sin\quad\left( {2m\quad\pi\quad\eta} \right)\quad\cos\quad\left( {2m\quad\pi\quad ɛ} \right)}{2m\quad\pi\quad\eta}} \right\rbrack}}} & (11)\end{matrix}$

For the antisymmetrical SH modes AS_(m), the corresponding formula is:$\begin{matrix}{R^{({AS}_{m})} = \sqrt{\eta\quad{\zeta\left\lbrack {1 - \frac{\sin\quad\left( {\left( {{2m}\quad + 1} \right)\quad\pi\quad\eta} \right)\quad\cos\quad\left( {\left( {{2m} + 1} \right)\quad\pi\quad\eta} \right)}{\left( {{2m} + 1} \right)\quad\pi\quad\eta}} \right\rbrack}}} & (12)\end{matrix}$

Since the formulae (5) and (6) for the reflection factor in a zerothapproximation contain all three relevant factors γ, 0 and . of the planemodel defect, with the modes SS_(m) with m=0 and AS_(m) both defectdetection and defect type classification are possible.

Lamb Modes.

The Lamb modes as solution of the boundary value problem of guidedelastic waves in an isotropic, homogeneous, non-piezoelectric, undampedplate are characterised in that there is an association between thelateral and the axial particle excursions, so that an ellipticallypolarised oscillation results.

As dispersion equation for the symmetrical Lamb modes there is obtained,according to

 F(Θ,γ;q):=(Θ−2)²cos(+γ√{square root over (qΘ−1)})sin(+γ√{square rootover (Θ−1)})+4√{square root over (qΘ−1)}√{square root over(Θ−1)}sin(+γ√{square root over (qΘ−1)})cos(+γ√{square root over(Θ−1)})=0  (13)

an implicit functional equation for 1=1((;q), which however cannot beexplicitly represented analytically. If we investigate the functionalequation (13) by means of the theory of functions, we find that thereare infinitely enumerable function branches, which do not intersectanywhere and which could therefore be unambiguously numbered inincreasing order. Analogously to the SH modes, we therefore do notconsecutively number the dimensionless eigenvalues 1, but—beginning atzero—the associated eigensolutions. We shall denote these symmetricalLamb modes by S_(m).

The reflection factor for the symmetrical Lamb modes S_(m) is obtainedas a zeroth approximation as $\begin{matrix}{R^{(S_{m})} = \sqrt{\zeta\quad\frac{Z^{(S_{m})}}{N^{(S_{m})}}}} & (14)\end{matrix}$

For the auxiliary values appearing in (14) the relationships:$\begin{matrix}\begin{matrix}{Z^{(S_{m})} = {{4\quad\gamma\quad\eta\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)\quad\left( {{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right)\quad\sin^{2}\quad\left( {{+ \gamma}\quad\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} + {\gamma\quad\eta\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)\quad{\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)^{2} \cdot}}}} \\{{\sin^{2}\quad\left( {{+ \gamma}\quad\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} + {2\quad\left( {{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right)\quad\left( {{3\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 4} \right)\quad\sin^{2}\quad{\left( {{+ \gamma}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot}}} \\{{\frac{\sin\quad\left( {{+ 2}\quad\gamma\quad\eta\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}\quad\cos\quad\left( {{+ 2}\quad\gamma\quad ɛ\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} + \left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - {4q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} + 4} \right)} \\{\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)^{2}\quad\sin^{2}\quad\left( {{+ \gamma}\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)\quad\frac{\sin\quad\left( {{+ 2}\quad\gamma\quad\eta\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}{{+ 2}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}} \\{{{\cos\quad\left( {{+ 2}\quad\gamma\quad ɛ\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} - {2\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - {2q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} + 4} \right)}}\quad} \\{\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}\quad{\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \cdot \sin}\quad\left( {{+ \gamma}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)\quad\sin\quad{\left( {{+ \gamma}\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot}} \\{\left\{ {\frac{\sin\left\lbrack {\gamma\quad\eta\quad\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}\quad{\cos\left\lbrack {\gamma\quad ɛ\quad\left( {{+ \sqrt{\quad{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}} -} \right.} \right.}} \right.} \\{\left. \left. \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right) \right\rbrack + \frac{\sin\left\lbrack {\gamma\quad\eta\quad\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}} \\{\left. {\cos\left\lbrack {\gamma\quad ɛ\quad\left( {{+ \sqrt{\quad{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack} \right\} + {2\quad\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)\quad\left( {{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right)}} \\{\left( {4 - {\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)}} \right)\quad\sin\quad{\left( {{+ \gamma}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot \sin}\quad{\left( {{+ \gamma}\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot}} \\{\left\{ {\frac{\sin\left\lbrack {\gamma\quad\eta\quad\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}\quad{\cos\left\lbrack {\gamma\quad ɛ\quad\left( {{+ \sqrt{\quad{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}} -} \right.} \right.}} \right.} \\{\left. \left. \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right) \right\rbrack - \frac{\sin\left\lbrack {\gamma\quad\eta\quad\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}} \\\left. {\cos\left\lbrack {\gamma\quad ɛ\quad\left( {{+ \sqrt{\quad{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack} \right\}\end{matrix} & (15) \\{and} & \quad \\\begin{matrix}{N^{(S_{m})} = {{4\quad\gamma\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)\quad\left( {{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right)\quad\sin^{2}\quad\left( {{+ \gamma}\quad\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} + {\gamma\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)\quad{\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)^{2} \cdot}}}} \\{{\sin^{2}\quad\left( {{+ \gamma}\quad\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} + {2\quad\left( {{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right)\quad\left( {{3\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 4} \right)\quad\sin^{2}\quad{\left( {{+ \gamma}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot}}} \\{\frac{\sin\quad\left( {{+ 2}\quad\gamma\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}{\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}\quad + \left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - {4q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} + 4} \right)} \\{{{\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)^{2} \cdot \sin^{2}}\quad\left( {{+ \gamma}\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)\quad\frac{\sin\quad\left( {{+ 2}\quad\gamma\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}{{+ 2}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}}\quad -} \\{2\quad\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)\quad\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - {2q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} + 4} \right)\quad\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}\quad\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \\{{\sin\quad{\left( {{+ \gamma}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot \quad{\sin\left( {{+ \gamma}\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \cdot}}\quad} \\{\left\{ {\frac{\sin\left\lbrack {\gamma\quad\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} +} \right.} \\{\left. \frac{\sin\left\lbrack {\gamma\quad\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\} + \quad{\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)\quad\left( {{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right)}} \\{2\quad\left( {4 - {\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)}} \right)\quad\sin\quad{\left( {{+ \gamma}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot \sin}\quad{\left( {{+ \gamma}\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot}} \\{\left\{ {\frac{\sin\left\lbrack {\gamma\quad\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}\quad -} \right.} \\\left. \frac{\sin\left\lbrack {\gamma\quad\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}\quad \right\}\end{matrix} & (16)\end{matrix}$apply.

Since the formulae (14) to (16) for the reflection factor of thesymmetrical Lamb modes S_(m) as a zeroth approximation contain theparameter, explicitly and the two parameters 0 and γ implicitly, withthese modes both defect detection and also defect type classificationare possible.

For the antisymmetrical Lamb modes A_(m) the corresponding formulae canbe derived in strictly analogous manner to the formulae (14) to (16). Itis then also the case for the antisymmetrical Lamb modes that with themboth a defect detection and a defect type classification is possible. Itis preferred to use the mode A₀, since here the conversion into practicegives the cleanest measuring signal, since they do not have “foreignmode signals” of symmetrical modes superimposed on them.

1. A method for testing solid bodies using guided ultrasonic waves,comprising: producing a first guided ultrasonic wave in a solid body bymeans of an ultrasonic transmitter, the first guided ultrasonic wavehaving a first mode; detecting reflection waves of the first guidedultrasonic wave by an ultrasonic receiver; producing a second guidedultrasonic wave in the solid body by means of the ultrasonictransmitter, the second guided ultrasonic wave having a second mode;detecting reflection waves of the second guided ultrasonic wave by theultrasonic receiver; determining structures of defects in material ofsolid body by combination of detected values of the reflection waves ofthe first guided ultrasonic wave and the second guided ultrasonic wave;and accelerating and evaluation of a defect by converting all reflectionvalues of the reflection values of the reflection waves in an expectedregion into defect values before measurement and wherein measurementcomprises a comparison of the measured reflection values with previouslycalculated values.
 2. A method as claimed in claim 1, wherein the firstand second waves are plate waves.
 3. A method as claimed in claim 2,further comprising performing a determination of a type and adetermination of a size of material defects.
 4. A method for testingsolid bodies using guided ultrasonic waves, comprising: producing afirst guided ultrasonic plate wave in a solid body by means of anultrasonic transmitter, the first guided ultrasonic plate wave having afirst mode; detecting reflection waves of the first guided ultrasonicplate wave by an ultrasonic receiver; producing a second guidedultrasonic plate wave in the solid body by means of the ultrasonictransmitter, the second guided ultrasonic plate wave having a secondmode; detecting reflection waves of the second guided ultrasonic wave bythe ultrasonic receiver; determining structures or defects in materialof the solid body by combination of detected values of the reflectionwaves of the first guided ultrasonic plate wave and the second guidedultrasonic plate wave; and determining a type and a size of the defectsby means of the following relationships: $\begin{matrix}{Z^{(S_{m})} = {{4\quad\gamma\quad\eta\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)\left( {{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right)\sin^{2}\quad\left( {{+ \gamma}\quad\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} + {\sin^{2}\quad\left( {{+ \gamma}\quad\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} +}} \\{2\quad\left( {{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right)\quad\left( {{3\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 4} \right)\quad\sin^{2}\quad{\left( {{+ \gamma}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot \quad\frac{\sin\quad\left( {{+ 2}\quad\gamma\quad\eta\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}}} \\{{{\cos\quad\left( {{+ 2}\quad\gamma\quad ɛ\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} + {\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - {4q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} + 4} \right)\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)^{2}}}\quad} \\{{\sin^{2}\quad\left( {{+ \gamma}\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)\quad\frac{\sin\quad\left( {{+ 2}\quad\gamma\quad\eta\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}{{+ 2}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}\quad\cos\quad\left( {{+ 2}\quad\gamma\quad ɛ\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} -} \\{2\quad\left( {{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)\quad\left( {{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - {2q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} + 4} \right)\quad\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}\quad{\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \cdot}} \\{{\sin\quad\left( {{+ \gamma}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)\quad{{\sin\left( {\gamma\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \cdot}}\quad} \\{\left\{ {\frac{\sin\left\lbrack {\gamma\quad\eta\quad\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}\quad{\cos\left\lbrack {\gamma\quad ɛ\quad\left( {{+ \sqrt{\quad{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}} -} \right.} \right.}} \right.} \\{\left. \left. \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right) \right\rbrack + \frac{\sin\left\lbrack {\gamma\quad\eta\quad\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}} \\{{\left. {\cos\left\lbrack {\gamma\quad ɛ\quad\left( {{+ \sqrt{\quad{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack} \right\} + {2\quad\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)\quad\left( {{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right)}}\quad} \\{\left( {4 - {\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)}} \right)\quad\sin\quad{\left( {{+ \gamma}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot {\sin\left( {{+ \gamma}\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \cdot}} \\{\left\{ {\frac{\sin\left\lbrack {\gamma\quad\eta\quad\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}\quad{\cos\left\lbrack {\gamma\quad ɛ\quad\left( {{+ \sqrt{\quad{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}} -} \right.} \right.}} \right.} \\{\left. \left. \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right) \right\rbrack - \frac{\sin\left\lbrack {\gamma\quad\eta\quad\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {{+ \sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}} \\\left. {~~}{\cos\left\lbrack {\gamma\quad ɛ\quad\left( {{+ \sqrt{\quad{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack} \right\}\end{matrix}$ and $\begin{matrix}{N^{(S_{m})} = {{4\quad\gamma\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)\quad\left( {{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right)\quad\sin^{2}\quad\left( {{+ \gamma}\quad\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} + {\gamma\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)\quad{\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)^{2} \cdot}}}} \\{{\sin^{2}\quad\left( {{+ \gamma}\quad\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} + {2\quad\left( {{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right)\quad\left( {{3\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 4} \right)\quad\sin^{2}\quad{\left( {{+ \gamma}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot}}} \\{\frac{\sin\quad\left( {{+ 2}\quad\gamma\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}{\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}\quad + {\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - {4q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} + 4} \right){\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)^{2} \cdot}}} \\{{\sin^{2}\quad\left( {{+ \gamma}\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)\quad\frac{\sin\quad\left( {{+ 2}\quad\gamma\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}{{+ 2}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}}}\quad -} \\{2\quad\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)\quad\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - {2q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} + 4} \right)\quad\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}\quad\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \\{\sin\quad{\left( {{+ \gamma}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot \quad\sin}\quad{\left( {{+ \gamma}\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot}} \\{\left\{ {\frac{\sin\left\lbrack {\gamma\quad\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} + \frac{\sin\left\lbrack {\gamma\quad\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}} \right\} +} \\{2\quad\left( {{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 2} \right)\quad\left( {{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} \right)\quad\left( {4 - {\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)}} \right)\quad\sin\quad{\left( {{+ \gamma}\sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot}} \\{\sin\quad{\left( {{+ \gamma}\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right) \cdot}} \\{\left\{ {\frac{\sin\left\lbrack {\gamma\quad\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} - \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}\quad - \frac{\sin\left\lbrack {\gamma\quad\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)} \right\rbrack}{\left( {\sqrt{{\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1} + \sqrt{{q\quad\Theta^{(S_{m})}\quad\left( {\gamma;q} \right)} - 1}} \right)}}\quad \right\}}\end{matrix}$
 5. A method for testing solid bodies using guidedultrasonic waves, comprising: producing a first guided ultrasonic platewave in a solid body by means of an ultrasonic transmitter, the firstguided ultrasonic plate wave having a first mode; detecting reflectionwaves of the first guided ultrasonic plate wave by an ultrasonicreceiver; producing a second guided ultrasonic plate wave in the solidbody by means of the ultrasonic transmitter, the second guidedultrasonic plate wave having a second mode; detecting reflection wavesof the second guided ultrasonic wave by the ultrasonic receiver;determining structures or defects in material of the solid body bycombination of detected values of the reflection waves of the firsguided ultrasonic plate wave and the second guided ultrasonic platewave; and bringing a measure value of a defect into relationship with areference echo in the solid body to form a relative measure value, andusing the relative measured value to determine a type and a size of thedefect.
 6. A method as claimed in claim 1, wherein the waves comprise onof tube or bar waves.
 7. A method as claimed in claim 1, wherein thefirst wave is a Lamb wave and the second wave is an SH wave.
 8. A methodas claimed in claim 7, wherein the Lamb wave is a S-0 wave and the SHwave is an S-1 wave.